Access with AmEx DR only applies when flying DL same day; so far, SC membership gets you in regardless of the airline you're flying. DR access and SC membership are both supposed to allow two guests, but the BE ATL E club dragon told me otherwise in January.

You might want to consider trading your AmEx DR card for the regular AmEx Platinum Charge Card (not the AmEx Delta Skymiles Platinum Credit Card) for about the same annual fee. You would get Membership Rewards points on total spend rather than DL Skymiles. This gives you DL SC access when flying DL same day and CO PC access when flying CO same day, including two guests. The same holds for a thrid airline--I think it's currently AA. Note that codeshares do not count.

Priority Pass gets you into many CO PCs (but no DL SCs) and other lounges worldwide. Their cheapest package is about $130 per year plus $30 per visit per person. Most lounges allow two guests (or sometimes the entire family); frequently children are free.